Integer-order disturbance observer based hybrid synchronization of SEIR Tuberculosis System using Active Control

Resumen

This paper presents an investigation of chaos control and synchronization in an integer-order non
linear SEIR tuberculosis (TB) system using the active control method. The model describes the transmission
dynamics of tuberculosis through four interacting compartments, that is, susceptible, exposed, infectious and
recovered — whose non-linear coupling leads to chaotic oscillations under certain parameter conditions. Such
chaotic behaviour reflects the inherent complexity and unpredictability of disease spread within a population.
To suppress this chaotic behaviour and achieve synchronization, an active control approach is developed using
master–slave framework. In this paper, the slave system is influenced by constant but bounded external
disturbances, while suitable control inputs are applied to stabilize the dynamics. A Lyapunov-based stability
analysis is performed to establish sufficient conditions for the asymptotic convergence of synchronization errors.
The analysis confirms that the controlled system remains stable and robust even in the presence of constant
disturbances. Numerical simulations further demonstrate that the designed controller effectively eliminates
chaotic oscillations, ensures complete synchronization of the system states and maintains smooth and stable
trajectories. Overall, the results validate that the active control method provides an efficient and reliable
means of controlling chaos and achieving synchronization in non-linear integer-order tuberculosis system. This
approach can be adapted to a broad class of biological and engineering systems exhibiting similar non-linear
and chaotic characteristics.